Modelling of drying processes without adjustable parameters is still a challenge. As emphasized in several previous works, this might partly be due to the impact of liquid films trapped in corners of the pore space. In this study, we present and analyse a drying experiment with a micromodel, which clearly shows the presence of corner films. In contrast with previous works, however, the corner films do not form a system of interconnected corner films extending over large regions in our micromodel. They rather form isolated capillary rings surrounding the solid blocks of the device, and thus, a quasi-two-dimensional version of liquid bridges often observed in the contact regions between grains in soils and packings of particles. These capillary rings essentially remain confined in the two-phase region. As a result, their impact on drying rate is much smaller than in systems favouring films hydraulically connected over long distances. The capillary liquid ring formation is taken into account in a pore network model of drying leading to satisfactory agreement with the experiment provided that the lateral pinning of liquid phase observed in the experiment is included in the model. Based on this, the model enriches the family of pore network models of drying and can be considered as a step towards the modelling of secondary capillary effects in drying in more complex geometry.tot Total evaporation surface area (m 2 ) A t Cross-sectional area of throats (m 2 ) A r Ring evaporation surface area (m 2 ) h Film height (m) L Lattice spacing (m) L r Ring width (m) L d Network depth (m) M Molar mass (kg kmol −1 ) M Mass flow rate (kg s −1 ) P Total pressure (Pa) P c Capillary pressure (Pa) P l Liquid pressure (Pa) P v Vapour pressure (Pa) P * v Saturation vapour pressure (Pa) P v,∞ Vapour pressure in the bulk air phase (Pa) r t Throat radius (m) r t Mean throat radius (m) r t,d Meniscus radius at ring detachment (m) R Universal gas constant (kJ kmol −1 K −1 ) s BL Boundary layer thickness (m) S Total network saturation (-) t Time (s) T Temperature ( • C) T Mean temperature ( • C) V Volume (m 3 )Greek symbols α Fitting parameter (-) δ Diffusivity (m 2 s −1 ) θContact angle (-) σSurface tension (N m −1 )

In this study, isothermal and non-isothermal drying experiments with imposed constant temperature gradients have been conducted in a two-dimensional square pore network of borosilicate glass (SiO 2 ) with interconnected etched channels. In experiments with temperature decreasing from the open surface of the pore network, a travelling stabilized gas-liquid region could be established, while in isothermal experiments with uniform temperature faster breakthrough and an extended two-phase zone were observed. Both findings are in good agreement with pore network simulations. However, numerical underestimation of drying rates (especially in the second period of drying) indicates that liquid films might play a major role in the experimental pore networks, even in the presence of thermal gradients.

Evaporation—a key process for water exchange between soil and atmosphere—is controlled by internal water fluxes and surface vapor fluxes. Recent studies demonstrated that the dynamics of the water flow in corners determine the time behavior of the evaporation rate. The internal water flux of the porous media is often described by capillary flow assuming complete wetting. Particularly, the crucial influence of partial wetting, that is, the nonlinear contact angle dependency of the capillary flow has been neglected so far. The focus of the paper is to demonstrate that SiO2‐surfaces can exhibit contact angles of about 40°. This reduces the internal capillary flow by 1 order of magnitude compared to complete wetting. First, we derived the contact angle by inverse modeling. We conducted a series of evaporation experiments in a 2‐D square lattice microstructure connected by lognormal distributed throats. We used an explicit analytical power series solution of the single square capillary model. A contact angle of 38° ± 1° was derived. Second, we directly measured the contact angle of the Si‐SiO2 wafer using the Drop Shape Analyzer Krüss 100 and obtained an averaged contact angle of 42° ± 2°. The results support the single square capillary model as an appropriate model for the description of the evaporation process in an ideal square capillary.

Pore network models are powerful tools to simulate invasion and transport processes in porous media. They are widely applied in the field of geology and the drying of porous media, and have recently also received attention in fuel cell applications. Here we want to describe and discuss how pore network models can be used as a prescriptive tool for future water electrolysis technologies. In detail, we suggest in a first approach a pore network model of drainage for the prediction of the oxygen and water invasion process inside the anodic porous transport layer at high current densities. We neglect wetting liquid films and show that, in this situation, numerous isolated liquid clusters develop when oxygen invades the pore network. In the simulation with narrow pore size distribution, the volumetric ratio of the liquid transporting clusters connected between the catalyst layer and the water supply channel is only around 3% of the total liquid volume contained inside the pore network at the moment when the water supply route through the pore network is interrupted; whereas around 40% of the volume is occupied by the continuous gas phase. The majority of liquid clusters are disconnected from the water supply routes through the pore network if liquid films along the walls of the porous transport layer are disregarded. Moreover, these clusters hinder the countercurrent oxygen transport. A higher ratio of liquid transporting clusters was obtained for greater pore size distribution. Based on the results of pore network drainage simulations, we sketch a new route for the extraction of transport parameters from Monte Carlo simulations, incorporating pore scale flow computations and Darcy flow.

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In an article published in 2008 [1] , Professor A.R. Mujumdar and his colleagues reviewed some applications of fractal concept on drying. As a modest continuation to this article, we give an overview on three drying related issues where fractal aspects are present. First, we discuss within the framework of the theory of invasion percolation in a gradient the characteristic lengths that determine the extent of the hydraulically connected region during drying. It is pointed out that the scaling of this region is fundamentally different in 2D and in 3D owing to the different percolation properties in 2D and 3D. In particular, it is shown that the fractal region only represents a small region of a drying front in 3D systems. Then a situation is described where fractal porous structures form as a result of an evaporation process. Finally we consider drying in systems characterized by an initial fractal distribution of the liquid phase (invasion percolation cluster), a situation expected to happen in PEM fuel cells, and explore the size dependent property of the overall drying time from pore network simulations.

Recently, pore network modelling has been attracting attention in the investigation of electrolysis. This study focuses on a 2D pore network model with the purpose to study the drainage of water by oxygen in anodic porous transport layers (PTL). The oxygen gas produced at the anode catalyst layer by the oxidation of water flows counter currently to the educt through the PTL. When it invades the water-filled pores of the PTL, the liquid is drained from the porous medium. For the pore network model presented here, we assume that this process occurs in distinct steps and applies classical rules of invasion percolation with quasi-static drainage. As the invasion occurs in the capillary-dominated regime, it is dictated by the pore structure and the pore size distribution. Viscous and liquid film flows are neglected and gravity forces are disregarded. The curvature of the two-phase interface within the pores, which essentially dictates the invasion process, is computed from the Young Laplace equation. We show and discuss results from Monte Carlo pore network simulations and compare them qualitatively to microfluidic experiments from literature. The invasion patterns of different types of PTLs, i.e., felt, foam, sintered, are compared with pore network simulations. In addition to this, we study the impact of pore size distribution on the phase patterns of oxygen and water inside the pore network. Based on these results, it can be recommended that pore network modeling is a valuable tool to study the correlation between kinetic losses of water electrolysis processes and current density.

This is an author's version published in: http://oatao.univ-toulouse.fr/21468 To cite this version:Vorhauer, Nicole and Tsotsas, Evangelos and Prat, Marc Temperature gradient induced double stabilization of the evaporation front within a drying porous medium. (2018) Physical Review Fluids (3). 1-24. ISSN 2469-990X Official URL:https://doi.Drying of porous media very often occurs in the presence of significant temperature gradients because heat fluxes are imposed in many situations in order to decrease the drying time or to facilitate the moisture removal at a higher humidity of the surrounding gas phase. Here we consider the situation where the temperature increases with depth. We show from experiments with a micromodel that the temperature gradient induces the stabilization of the evaporation front within the model porous medium according to two different mechanisms occurring consecutively. The first mechanism occurs in the liquid phase and is explained by the dependence of surface tension upon temperature. This results in the preferential invasion of the warmer zones. The second mechanism occurs gas-sided due to the dependence of saturation vapor pressure upon temperature. We show that the time scales of both mechanisms are different leading to the temporary formation of distinctive phase patterns from which different periods of drying can be discriminated.